Chapter 9.1, Problem 73PE

A small grocer finds that the monthly sales $y$ (in $\text{\$}$ ) can be approximated as a function of the amount spent advertising on the radio $x_1$ (in $\text{\$}$ ) and the amount spent advertising in the newspaper $x_2$ (in $\text{\$}$ ) according to $y=a{x}_1+b{x}_2+c$ .

The table gives the amounts spent in advertising and the corresponding monthly sales for $3$ months.

a. Use the data to write a system of linear equations to solve for $a,b$ , and $c$ .

b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c. Write the model $y=a{x}_1+b{x}_2+c$ .

d. Predict the monthly sales if the grocer spends $\text{\$}2500$ advertising on the radio and $\text{\$}500$ advertising in the newspaper for a given month.